Construction of a Lax Pair for the E₆⁽¹⁾ q-Painlevé System
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Construction of a Lax Pair for the E₆⁽¹⁾ q-Painlevé System
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| Creator |
Witte, N.S.
Ormerod, C.M. |
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| Description |
We construct a Lax pair for the E₆⁽¹⁾ q-Painlevé system from first principles by employing the general theory of semi-classical orthogonal polynomial systems characterised by divided-difference operators on discrete, quadratic lattices [arXiv:1204.2328]. Our study treats one special case of such lattices - the q-linear lattice - through a natural generalisation of the big q-Jacobi weight. As a by-product of our construction we derive the coupled first-order q-difference equations for the E₆⁽¹⁾ q-Painlevé system, thus verifying our identification. Finally we establish the correspondences of our result with the Lax pairs given earlier and separately by Sakai and Yamada, through explicit transformations.
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| Date |
2019-02-18T17:56:05Z
2019-02-18T17:56:05Z 2012 |
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| Type |
Article
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| Identifier |
Construction of a Lax Pair for the E₆⁽¹⁾ q-Painlevé System / N.S. Witte, C.M. Ormerod // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 18 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 39A05; 42C05; 34M55; 34M56; 33C45; 37K35 DOI: http://dx.doi.org/10.3842/SIGMA.2012.097 http://dspace.nbuv.gov.ua/handle/123456789/148694 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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